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Stitz-Zeager_College_Algebra_e-book

# 7 8 9 x 7 8 x 53 other algebraic functions 3 325 y 1 e

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Unformatted text preview: striction on k −1 means we take the right half of the parabola. y 2 y = k(x) 1 −2 −1 1 −1 2 x y = k−1 (x) −2 Our last example of the section gives an application of inverse functions. Example 5.2.4. Recall from Section 2.1 that the price-demand equation for the PortaBoy game system is p(x) = −1.5x + 250 for 0 ≤ x ≤ 166, where x represents the number of systems sold weekly and p is the price per system in dollars. 1. Explain why p is one-to-one and ﬁnd a formula for p−1 (x). State the restricted domain. 2. Find and interpret p−1 (220). 3. Recall from Section 2.3 that the weekly proﬁt P , in dollars, as a result of selling x systems is given by P (x) = −1.5x2 + 170x − 150. Find and interpret P ◦ p−1 (x). 308 Further Topics in Functions 4. Use your answer to part 3 to determine the price per PortaBoy which would yield the maximum proﬁt. Compare with Example 2.3.3. Solution. 1. We leave to the reader to show the graph of p(x) = −1.5x + 250, 0 ≤ x ≤ 166, is a line segment from (0, 250) to (166, 1), and as such passes the Horizontal Line Test. Hence, p is − one-to-one. We ﬁnd the expression for p−1 (x)...
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